# What is 7+6i divided by 10+i?

##### 2 Answers

#### Answer:

# (7+6i)/(10+i) = 76/101 + 53/101i #

#### Explanation:

We can make the denominator real by multiplying the denominator with its complex conjugate, thus:

# (7+6i)/(10+i) = (7+6i)/(10+i) * (10-i)/(10-i)#

# " " = ( (7+6i)(10-i) ) / ( (10+i)(10-i) )#

# " " = ( 70-7i+60i-6i^2 ) / ( 100 -10i + 10i-i^2 )#

# " " = ( 70 + 53i +6 ) / ( 100 +1 )#

# " " = ( 76 + 53i ) / ( 101 )#

# " " = 76/101 + 53/101i#

#### Answer:

#### Explanation:

First we have to rationalize the denominator by multiplying the complex number in the denominator and the numerator by the denominator's conjugate.

**(using the difference of squares rule in the denominator)**

I hope that this helps.